Abstract
We consider birth-death processes taking values in N ≡ {0,1,... }, but allow the death rate in state 0 to be positive, so that escape from N is possible. Two such processes with transition functions { pij(t) } and { ̃pij(t) } are said to be similar if, for all i, j ∈ N, there are constants cij such that ̃pij(t) = cijpij(t) for all t ≥ 0. We determine conditions on the birth and death rates of a birth-death process for the process to be a member of a family of similar processes, and we identify the members of such a family. These issues are also resolved in the more general setting in which the two processes are called similar if there are constants cij and ν such that ̃pij(t) = cijeνtpij(t) for all t ≥ 0.
Original language | Undefined |
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Article number | 10.1239/jap/1014842840 |
Pages (from-to) | 835-849 |
Number of pages | 14 |
Journal | Journal of applied probability |
Volume | 2000 |
Issue number | 37 |
DOIs | |
Publication status | Published - 2000 |
Keywords
- invariant vector
- EWI-12851
- transition function
- METIS-140634
- Transient behaviour
- IR-62348
- Chain sequence
- Absorption probability